NOT gate at Porth Wen Brickworks

 

This gate is on the hill above Porth Wen Brickworks on Anglesey. I'm calling it a NOT gate because although the hinge is there and still turns, there is no gate. In electronics, a NOT gate is what is used to turn a 1 into a 0 or a 0 into a 1 in a logic circuit. On other words, what comes out is NOT what goes in; it is the opposite.

How to measure the diameter of a wire properly

 Notice that in these pictures I have the micrometer screw gauge first vertical and the horizontal. To get an accurate value for the diameter it is necessary to meaure at half a dozen places and take a mean. But it is also important to change the orientation of the gauge as it goes along.

Radial to linear on Mungrisdale Common

 

On Mungrisdale Common all paths converge on the summit cairn. They can be seen heading out like a radial field, like spokes on a wheel. However the panoramic view has mapped them into parallel lines.

Equalising the pressure on the beetroot

 Maybe it's old age creeping up on me, but I couldn't get the lid off the beetroot jar. Knowing that the pressure inside is lower than the pressure outside, I knocked a nail through the safety button. I was then able to open the jar. It seems that it was not just friction but was also the difference in pressure making it hard to open.

I gather that the food is cooked and then placed in the jar. The lid is screwed on. As the food cools, the air around it cools. The particles are not moving as fast so they don't collide with the lid as much. The pressure decreases. They also take up a smaller volume so the button, which is more flexble than the rest of the lid, is pulled in. By putting a hole in the lid, I allowed more particles in so there were more collisions raising the pressure inside to that outside.

How does air resistance affect a bullet?

I've been doing the maths on how the air resistance would affect the distance travelled by the bullet on the rifle range. I've used as the resultant force F the drag equation used in the previous post. A bit of calculus shows that the rate of change of velocity with distance depends on velocity, not velocity squared. Integration below shows that the factor is divided by mass, so maybe I've got the start of how ballistic coefficient is derived. 

If range would be when v = 0, then no proper inegral can be done because that would give the range as infinite in this model. So I have just worked on the idea that velocity decreases exponentially with distance. Mass of a .303 bullet is about 175 grams. Putting in the data I used in the last post, I made a spreadsheet to see what happened.

Over the length of the rifle range, air resistance makes very little difference so my calculation of a 5 metre drop for the bullet over the range should still stand. However I have not factored in that the bullet is supersonic.

Air resistance on the rifle range

 

Having done yesterday's calculation, I realised that I had neglected air resistance. I discovered that there is a complicated discipline called external ballistics but I've opted to try a simpler drag coefficient that I might understand. If viscous drag = 1/2 x density x velocity-squared x drag coefficient x cross-sectional area then if I use a drag coefficient of 0.3 (suggestion is that a bullet would be between 0.1 and 0.3) then I'd get drag force = 1/2 x 1.2 x 745^2 x 0.3 x 5 x 10^-5 = 4.6 Newtons. I calculated a cross-sectional area based on the .303 diameter bullet. More thinking to be done because it depends on speed so will decrease in size as the air resistance slows the bullet. It seems in the full analysis, they use something called ballistic coefficient instead of drag coefficient which seems to incorporate mass as well.

Applying suvat to the Great Mell Fell rifle range

 I finally got to visit the old rifle range behind Great Mell Fell.

The red-roofed building in the foreground is behind a wall and a bank of earth that would have been where the targets were placed.

The map shows that the whole range is 1km long from fence to fence. The actual firing distance would be shorter. I looked up the muzzle velocity of World War 2 rifles and 745m/s seems to be the British choice. So let's say the bullet was fired 745m down the range. It would take 1 second to hit the target. In that time it would be being pulled downwards by gravity. To calculate the fall I use s = ut + 1/2at^2. Acceration a = 9.81m/s^2. Initially it was falling vertically at 0m/s. So if t=1s, then s = 4.9m. That is much, much bigger than I was expecting!